$(102)^4=$ ?

$(102)^4=$ ?
  1. 108242316
  2. 108423216
  3. 102843216
  4. 108243216

Solution

$ \text { } \begin{aligned} (102)^4= & (100+2)^4 \\ = & { }^4 C_0(100)^4 \cdot 1+{ }^4 C_1(100)^3 \cdot 2^1 \\ & \quad+{ }^4 C_2(100)^2 \cdot 2^2+{ }^4 C_3(100)^1 \cdot 2^3 \\ & \quad+4 C_4(100)^0 2^4 \\ = & (100)^4+4(100)^3 \cdot 2+6(100)^2 \cdot 4 \\ & \quad+4(100) 8+1 \cdot 1 \cdot 16 \\ = & 100000000+8000000+240000 \\ = & 108243216 \end{aligned} $ Hence, option (4) is correct

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

Practice more Binomial Theorem questions on Aicharya